It all depends. I routinely shoot both calibers and my wife (at my strenuous urging) wanted a wheelgun and recently purchased one. She went with a Charter Arms Mag Pug in 357. (noted here about 6 weeks ago) Its all stainless, 2.2 inch barrel, and weighs about 26 ounces loaded. It has some kick using more potent 38+p rounds. After about 30 rounds in her hands I gave her some factory load 357 rounds. There were very strong to her but she handled them.
It is a lighter kick compared to a Taurus 738 TCP 380 auto. Wife had fired that 380 one time before and said No More for it. That 380 is a fair bit heavier recoil than my edc, a 9mm S&W 5906 4 inch barrel all stainless steel with a 15 round magazine on board. Of course weight difference is factor in there too. Full magazine makes it about 2.3 pounds.
It all depends on what fits her hand. As far as her first EDC weapon, get her a wheelgun. They are solid, reliable, simple easy to use and reload and basically point and shoot. If she is ever in an area where she needs needs more than 5 or 6 rounds, she should know not to be there before she goes.
Best recommendation from me-- Get her an all steel 357 wheelgun. Hammerless S&W or go with a hammer Charter Arms or about any reasonable brand. Hammered not S&W will be lower cost. Any one will work for her (IMHO) without significant issues. Load it with some Short Barrel 38+p rounds and let her try some of them. After working and using some WWB and various other brand 38 rounds. When I carry a 38 or 357 as CCW its with the 38+p rounds. Their lower recoil, faster back on target, muzzle blast and sufficient oomphf is why. Our edc 38 ammo is 135 grain Gold Dots.
Get a couple hundred WWB type rounds through her hands and a box or 2 of edc ammo and she will be good. Make sure she has Real Good Ear cover also. That is very strong factor in shooting learning.
Also get her to carry in a holster on her hip, armpit, bra strap, IWB, OWB, appendix or where ever other than in her purse. Pay a bit of attention to women's purses out in public. They keep close watch on them generally but fairly often turn their back, step away or that type stuff.
Grocery carts are notorious for that. Try watching and point it out to her on your next grocery shopping trip.
A purse grab or snatch is not a good thing to have happen when her weapon is in it.
Nemo